On partition functions of Gaussian random variables

Omer Friedland, Olivier Guédon, Fabien Souli

For $\beta \in \mathbb{R}$, we define the partition function $$Z_{\beta }(X)=\sum _{i=1}^N\exp (\beta X_i)$$ of a centered Gaussian random vector $X=(X_1,\dots ,X_N)$ with $\mathbb{E}[X_i^2]=…